In a torque converter provided with a lock-up clutch, control of the front/back differential pressure (lock-up differential pressure) of the lock-up clutch engages and disengages the lock-up clutch. When the torque converter shifts from a converter state to a lock-up state, the lock-up differential pressure may gradually rise from a predetermined initial differential pressure. In this case, the torque converter shifts from the converter state to the slip state via a lock-up state. In the converter state, the lock-up clutch is disengaged, in the slip state, the lock-up clutch slips, and in the lock-up state, the lock-up clutch is fully engaged. This prior art technology is disclosed for example in Tokkai 2004-138147 published by the Japan Patent Office in 2004.